This is from a 5970 manual, not a 5975, but because they are from the same company, a similar design approach is likely. The 5970 uses a turbomolecular pump, but regardless of the high vacuum pumping method, the concepts are the same.
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The vacuum system is controlled by the turbo controller. When proper vacuum has been achieved, the manifold heater relay can be activated. That, in turn, allows the detector electronics to be turned on so that the MSD can be used.
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The Heater/Electronics switch enables the manifold heater and the electronics but does NOT necessarily turn them on. The heater and electronics will turn on only after the turbomolecular pump reaches 50% of its maximum speed.
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There are no moving parts in a diffusion pump, so the speed of the pump can not be measured as it was with the 5970. But if the 5975 was designed in a manner similar to the 5970, the engineers would have placed some similar criterion on the state of the high vacuum system, quite possibly by measuring pressure or by sensing some other aspect of the diffusion pump operation.
There should be a heater at the bottom of your diffusion pump. You should be able to find it by looking for a fairly heavy duty electrical connection. The diffusion pump most likely also has a cooling jacket (and possibly a cold trap at the top) so, other than the heater area, it may feel cool.
Make sure that the diffusion pump is getting power. If it is, and the pump is cold, then you may have a problem with the pump's heater. If the heater is not getting power, then something is not allowing the heater to come on. Perhaps a failed relay, perhaps a loose wire, perhaps failed electronics. I would have to see a schematic to venture any more of a guess.
Don Baker